I received a lot of flack from some canoe snobs when I carpeted the inside of my cedar strip canoe several years ago.  It only took a few instances of a paddle or tackle box being dropped in the aluminum canoe across the lake for them to understand why I did this.  Yes, it added some weight but it kept the canoe that much more quiet.

Do this next time you are in open water:  Swim under your canoe and have someone else drop a jig on the canoe floor.  You can hear that "click" from a long distance.  And, no, I didn't use a wool woven burbur here.  Just the cheap outdoor "turf" like carpeting that added about 6lbs.